METABELIAN GROUPS WITH QUADRATIC DEHN FUNCTION AND BAUMSLAG–SOLITAR GROUPS

摘要

We prove that metabelian locally compact groups in a certain class have quadratic Dehn function. As an application, we embed the solvable Baumslag–Solitar groups in finitely presented metabelian groups with quadratic Dehn function. Also, we prove that Baumslag's finitely presented metabelian groups, in which the lamplighter groups embed, have quadratic Dehn function.